Flavopiridol is a flavone originally synthesized by Hoescht Pharmaceutical from a parent structure obtained from Dysoxylum binectariferum, a plant native to India. Flavopiridol has a novel structure compared with that of polyhydroxylated flavones including quercetin or genistein. This is a phase I study of flavopiridol, a drug that will be administered to cancer patients as a 72 hour intravenous infusion every two weeks. The study endpoint will be the determination of a maximum tolerated dose (MTD) that can be carried forward to phase II studies.